On Links, Functions, Integrals and 3-Manifold Invariants

The three things I hope you will remember on Monday after my talk are:

From an operative point of view, links look much like functions, and
if we knew how to integrate these functions, we'd have an invariant of
3-manifolds.

From an operative point of view, graphs look much like functions,
and the calculus of Feynman diagrams allows us to "integrate" certain
linear combinations of graphs.

Counting cosmic coincidences, we get a graph-valued invariant of
links (and hence of 3-manifolds).

Prerequisites: You need to know what's a link, a manifold, a graph, and an
integral. You don't need to know anything deep about these, though, and in
particular, you don't need to know anything about Feynman diagrams. In fact,
if you've never seen Feynman diagrams before and you are curious, today's
your chance!